Relativistic mechanics assumes distances and elapsed times need not be the same for all observers to have a consistent set of physics while Newtonian physics assumes that there is a universal space and time which all observers share and can measure identical distances and elapsed times in. Galilean relativity is a slight relaxation of Newtonian assumptions in that space and time need have no universally defined origin and state of absolute rest defined. Experiment has long shown that there is no preference for a state of absolute state of rest, so the absolute space and time of Newton appears to be unnecessary, and since at least 1859 experiments with fast-moving phenomena have been conducted which favor Special Relativity. But for slow-moving phenomena, the predictions of Newtonian or Galilean relativity are experimentally indistinguishable from those of Relativity. For velocities less than a tenth the speed of light, Newtonian Mechanics is about 99% accurate, and this gets better for lower speeds. Further while light can be described in a Newtonian framework, this description doesn't allow one to correctly describe how an experiment measuring light speed appears to a moving observer. But we all can't be unmoving observers. Frames of reference are significant, even in Galilean relativity, because different observers may disagree on when or even the order of events, but physics, is it is to mean anything, has to be legal for all observers and all observers must agree on the same laws of physics. Relativity was a big step in that direction.

But the remainder of your questions would seem to indicate that these answers are too high-level for your class. You had best hit the books and answer in your own words.